The Gregorian calendar is divided into months -- meaning moons, of course -- but it is a solar calendar; the months have no fixed relationship to the lunar cycle. The Islamic calendar is a true lunar calendar, but that means it has 354 day years, so that Islamic holidays have no consistent relationship to the seasons of the solar calendar. On the other hand, the Jewish calendar is lunisolar. Its months rigidly adhere to a lunar cycle, yet its festivals and holy days are required to follow the solar seasons. How is it done? Some astrophysical principles, some clever arithmetic, and rules -- lots and lots of rules.